Transfer entropy (TE) was introduced to overcome these shortcomings
 [1]}: if \(X\)  influences \(Y\) , then predicting \(Y\) 's future
becomes easier after knowing the present of both \(X\)  and \(Y\) , compared to only
knowing \(Y\) 's present. The TE from \(X\)  to \(Y\)  takes the form of a conditional
mutual information:
\(\mathcal {T}_{X\rightarrow Y}(\tau ) &= I(X_{t};Y_{t+\tau }|Y_{t}) \\& = H(Y_{t+\tau }|Y_{t})-H(Y_{t+\tau }|Y_{t},X_{t} )\nonumber ~.\) 
